Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,16,21,18,23,17,22)(14,19,25,34,27,36,26,35)(15,28,32,20,31,39,30,38)(24,40,29,33,42,37,41,43);(9,11)(12,14)(13,19)(15,29)(16,25)(17,26)(18,27)(20,37)(21,34)(22,35)(23,36)(24,30)(28,33)(31,41)(32,42)(38,40)(39,43);(12,15)(13,20)(14,24)(16,30)(17,32)(18,31)(19,33)(21,28)(22,39)(23,38)(25,41)(26,29)(27,42)(34,40)(35,37)(36,43);(9,11)(12,16,18,17)(13,21,23,22)(14,25,27,26)(15,30,31,32)(19,34,36,35)(20,28,38,39)(24,41,42,29)(33,40,43,37)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17391);